The cellular function of proteins, and their targeting by drug applications, are both governed by biomolecular thermodynamics and kinetics. In order to make meaningful and efficient predictions of these mechanisms, molecular simulations must be able to estimate the binding affinity and rates of association and dissociation of a protein-ligand complex, or the populations and rates of exchange between distinct conformational states (i.e. folding and unfolding, binding and unbinding). The above studies are typically done using different, but complementary approaches. Alchemical methods, including free energy perturbation (FEP) and thermodynamic integration (TI), have become the dominant method for computing high-quality estimates of protein-ligand binding free energies. In particular, the widely-used approach of relative binding free energy calculation can deliver accuracies within 1 kcal mol−1. However, detailed physical pathways and kinetics are missing from these calculations. In principle, all-atom molecular dynamics (MD) simulation, with the help of Markov State Models (MSMs), can be used to obtain this information, yet finite sampling error still limits MSM approaches from making accurate predictions for very slow unfolding or unbinding processes. To overcome these issues, a new approach called multiensemble Markov models (MEMMs) have been developed, in which sampling from biased thermodynamic ensembles can be used to infer states populations and transition rates in unbiased ensembles. In this dissertation, two distinct biophysical problems are investigated. In the first part, we apply expanded ensemble (EE) methods to accurately predict relative binding free energies for a series of protein-ligand systems. Moreover, we propose a simple optimization scheme for choosing alchemical intermediates in free energy simulations. In the second part, we employ MEMMs to estimate the free energies and kinetics of protein folding and ligand binding, to achieve greatly improved predictions. Finally, we combine the above EE method and a maximum-caliber algorithm to study how sequence mutations perturb protein stability and folding kinetics. In summary, this work comprises a wide range of current methodology in biophysical simulation, complementing and improving upon existing approaches.